ESSAYS on the CROSS-SECTION of RETURNS Lu Zhang a DISSERTATION in Finance for the Graduate Group in Managerial Science and Appli
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ESSAYS ON THE CROSS-SECTION OF RETURNS Lu Zhang A DISSERTATION in Finance for the Graduate Group in Managerial Science and Applied Economics Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2002 Supervisor of Dissertation Graduate Group Chairperson Dedication To my parents, for teaching me the value of knowledge. ii Acknowledgments I am grateful to my advisor, Craig MacKinlay, for his kindness, support, and exceptional guidance, and to the rest of my dissertation committee — Andrew Abel, Amir Yaron, Leonid Kogan, and especially Joao Gomes — for their collective insight and encourage- ment. I would also like to express my gratitude to several other faculty — Michael Brandt, Domenico Cuoco, Gary Gorton, Michael Gibbons, Skander Van den Heuvel, Donald Keim, Nick Souleles, and Rob Stambaugh — for their roles in creating a supportive and exciting environment for learning. iii ABSTRACT ESSAYS ON THE CROSS-SECTION OF RETURNS Lu Zhang A. Craig MacKinlay My dissertation aims at understanding the economic determinants of the cross-section of equity returns. It contains three chapters. Chapter One constructs a dynamic general equilibrium production economy to explic- itly link expected stock returns to firm characteristics such as firm size and the book- to-market ratio. Despite the fact that stock returns in the model are characterized by an intertemporal CAPM with the market portfolio as the only factor, size and book-to- market play separate roles in describing the cross-section of returns. However, these firm characteristics appear to predict stock returns only because they are correlated with the true conditional market beta. Moreover, quantitative analysis suggests that these cross- sectional relations can subsist even after one controls for a typical empirical estimate of market beta. This lends support to the view that the documented ability of size and book- to-market to explain the cross-section of stock returns is consistent with a single-factor conditional CAPM model. Chapter Two asks whether firms’ financing constraints are quantitatively important in explaining asset returns. It has two main findings. First, for a large class of theoretical models, financing constraints have a parsimonious representation amenable to empirical analysis. Second, financing frictions lower both the market Sharpe ratio and the correla- tion between the pricing kernel and returns. Consequently, they significantly worsen the performance of investment-based asset pricing models. These findings question whether iv financing frictions are important for explaining the cross-section of returns and whether they provide a realistic propagation mechanism in several macroeconomic models. Chapter Three proposes a novel economic mechanism underlying the value premium, the average return difference between value and growth stocks in the cross-section. The key element emphasized is the asymmetric adjustment cost of capital. During recessions, value firms face more difficulty than growth firms in downsizing capital, and hence their dividend streams fluctuate more with economic downturns. The upshot is that value stocks are more risky than growth stocks in bad times. An industry equilibrium model shows that this mechanism, when combined with a countercyclical market price of risk, goes a long way in generating a value premium that is quantitatively comparable to that observed in the data. v Contents Dedication....................................... ii Acknowledgments................................... iii Abstract........................................ iv 1 Equilibrium Cross-Section of Returns 1 1.1Introduction................................... 1 1.2TheModel................................... 3 1.2.1 The Economy and the Competitive Equilibrium . ........ 4 1.2.2 AssetPrices............................... 14 1.3AggregateStockReturns............................ 20 1.3.1 Calibration............................... 20 1.3.2 QuantitativeResults.......................... 21 1.4TheCross-SectionofStockReturns..................... 23 1.4.1 Calibration............................... 23 1.4.2 SimulationandEstimation...................... 25 1.4.3 SizeandBook-to-MarketEffects................... 26 1.4.4 BusinessCycleProperties....................... 30 1.5Conclusion................................... 34 vi 2 Asset Pricing Implications of Firms’ Financing Constraints 57 2.1Introduction................................... 57 2.2 Investment Based Asset Pricing with Costly External Finance . 60 2.2.1 Modelling Financing Frictions . .................... 61 2.2.2 Firm’sProblem............................. 63 2.2.3 AssetPricingImplications....................... 64 2.3InvestmentBasedFactorPricingModels................... 67 2.3.1 AssetPricingTests........................... 67 2.3.2 EconometricMethodology....................... 69 2.3.3 Data................................... 71 2.4Results...................................... 72 2.4.1 GMMEstimates............................ 72 2.4.2 TheEffectofFinancingConstraints................. 74 2.5Robustness................................... 77 2.5.1 SmallFirmsEffects.......................... 77 2.5.2 Fama-FrenchPortfolios........................ 77 2.5.3 Different Macroeconomic Data .................... 78 2.5.4 Non-Linear Pricing Kernels . .................... 78 2.5.5 AlternativeCostFunctions...................... 78 2.6Conclusion................................... 79 2.7 Data Construction ................................ 88 3 The Value Premium 97 3.1Introduction................................... 97 3.2RelatedLiterature............................... 100 vii 3.3TheModel................................... 102 3.3.1 TheEnvironment............................ 102 3.3.2 TheFirms................................ 105 3.3.3 AggregationandHeterogeneity.................... 109 3.3.4 Recursive Competitive Equilibrium . ................ 110 3.3.5 Computational Strategy ........................ 111 3.4Findings..................................... 112 3.4.1 Calibration............................... 112 3.4.2 QualityofApproximateAggregation................. 115 3.4.3 TimeSeries............................... 115 3.4.4 Cross-Section.............................. 116 3.4.5 Intuition................................. 117 3.4.6 QuantifyingtheSurvivalBias..................... 121 3.5Conclusion................................... 123 viii List of Tables 1.1 : Parameter Values Used in Simulation ................ 43 1.2 : Moments of Key Aggregate Variables ................ 43 1.3 : Book-To-Market As a Predictor of Market Returns ....... 44 1.4 : Properties of Portfolios Formed on Size ............... 45 1.5 : Properties of Portfolios Formed on Book-to-Market ....... 46 1.6 : Average Returns For Portfolios Formed on Size (Down) and then β (Across) ............................... 47 1.7 : Exact Regressions ............................. 48 1.8 : Fama-French Regressions ........................ 49 1.9 : Cross-Sectional Correlations ...................... 49 1.10 : Exact Regressions — Sensitivity Analysis .............. 50 1.11 : Fama-French Regressions — Sensitivity Analysis ......... 51 1.12 : Cross-Sectional Return Dispersion As a Predictor of Market Volatility .................................... 52 2.1 : Summary Statistics of the Assets Returns in GMM ....... 89 2.2 : GMM Estimates and Tests — The Benchmark .......... 90 2.3 : Properties of Pricing Kernels, Jensen’s α, and Investment Returns 91 ix 2.4 : GMM Estimates and Tests — Alternative Moment Conditions 92 2.5 : GMM Estimates and Tests — Alternative Measures of Profits 93 2.6 : GMM Estimates and Tests — Alternative Specifications .... 94 3.1 : Benchmark Parameterization ..................... 137 3.2 : Key Moments Under Benchmark Parameterization ....... 138 3.3 : Aggregate Book-to-Market As a Predictor of Market Returns 138 3.4 : Properties of Portfolios Formed on Size ............... 139 3.5 : Properties of Portfolios Formed on Book-to-Market ....... 140 3.6 : Summary Statistics of HML and SMB ................ 140 3.7 : Risk and Asymmetric Adjustment Cost ............... 141 3.8 : The Magnitude of Survival Bias .................... 141 x List of Figures 1.1 : Some Key Variables in Competitive Equilibrium ......... 53 1.2 : Size and Book-to-Market in Cross-sectional Regressions .... 54 1.3 : Business Cycle Properties: I ...................... 55 1.4 : Business Cycle Properties: II ..................... 56 1.5 : Return Dispersion over Business Cycle ............... 56 2.1 : Predicted Versus Actual Mean Excess Returns .......... 95 2.2 : Correlation Structure ........................... 96 3.2 : Countercyclical Market Price of Risk ................ 143 3.3 : Value Factor in Earnings ........................ 143 xi Chapter 1 Equilibrium Cross-Section of Returns with Joao F. Gomes and Leonid Kogan 1.1 Introduction The cross-sectional properties of stock returns have attracted considerable attention in recent empirical literature in financial economics. One of the best known studies, by Fama and French (1992), uncovers the relations between factors such as book-to-market ratio and firm size and stock returns, which appear to be inconsistent with the standard Capital Asset Pricing Model (CAPM). Despite their empirical success, these simple statistical relations have proved very hard to rationalize and their precise economic source remains a subject of debate.1 The challenge posed by the Fama and French (1992) findings to traditional